Until this point, the arguments above have proceeded in parallel to those in [1]}. The improvement over [1]} comes from properly choosing \(s\)  and \(\gamma \) ; we choose \(s\)  and \(\gamma \)  so that
\(s = \left(K_1^3K_2^2K_3 \delta ^{3\alpha /2}\right)^{2/(\alpha +2)},\quad \delta ^{\gamma } = K_3^{1/\alpha }\delta ^{1/2}s^{-1/2}.\) 
